1. (W)Where (Understanding), Why (Real Life), and What (MLR and Product) 2. (H)Hook (Engage) 3. (E)Equip (Instruction), Explore (Graphic Organizer), and Experience (Cooperative Learning) 4. (R)Rethink, Revise, Rehearse, and Refine (Timely Feedback) 5. (E)Evaluate (Self- Assessment) 6. (T) Tailor (Multiple Intelligences 6 to 8 and use each at least twice) 7. (O)Organize (Facet of Understanding)
Lesson 1
Consider the W.H.E.R.E.T.O. elements. (L)
1. Students will understand how polynomial expressions can be solved by using the horizontal, vertical or FOIL methods. (Where) This lesson is important to real life because it will give students the necessary options to help them choose which method comes most naturally to them. (Why)Studentsunderstand and use polynomials and expressions with rational exponents. (What) Product: Wiki entry about which method works best for which application with examples.
2. Read a poem aloud about math methods. (Hook)
3. Students should know the following terminology: "like" terms, polynomial, FOIL method, leading and constant term and polynomial function. Students should be able to at least add basic binomial expressions. (Equip) The beginning of the class will be a discussion and students with work in pairs discussing their wiki entry. (Explore) Students will share their examples with the rest of the class to show how each method can be used. (Experience)
4. The students will comment on each others' entries and say whether they agree or disagree and why; this will make students look at someone else's perspective. (Re-think) Students will have the opportunity to edit their entry should their peers' comments sway them. (Revise) Students will have to come up with examples of methods. (Rehearse) Students will be able to fix all grammatical and technical errors in wiki entries to receive full credit. (Refine)
5. Wiki reflection, KWL chart (Evaluate)
6. Mathematical/ Reasoning: Students will have to give examples on the wiki and why they work best. Interpersonal: Students will be working in pairs on wiki entries. Intrapersonal: Students will individually comment on their peers' wikis. Spacial/ Visual: Students will take notes on the different methods shown written out on the board. Verbal/ Linguistic: Students will be writing a small paragraph about math methods. Musical/ Rhythmic: Students will listen to a poem about math. (Tailor)
7. Students will be able to illustrate how polynomial expressions can be solved using the horizontal, vertical or FOIL methods. (Organize)
Lesson 2
Consider the W.H.E.R.E.T.O. elements. (L)
8. Students will understand how visual representations are used to solve and express polynomial expressions. (Where) This lesson is important to real life because it will connect the physical outside world to polynomials. (Why) Studentsunderstand and use polynomials and expressions with rational exponents. (What) Product: PowerPoint interactive, algebraic Tic-Tac-Toe boards
9. Draw a rectangle on the board and ask students to define what it is and what it could be. (Hook)
10. Students should know terminology: polynomial and "like" terms. Students should be able to solve basic polynomial expressions. (Equip) The beginning of the class will be a class discussion. (Explore) Students will present their Tic-Tac-Toe boards to show their understanding as an artifact that proves that they understand how a visual representation can be used to solve or express polynomial expressions. (Experience)
11. The presentation will force them to explain how they were able to figure out what box had to contain which equation. (Re-think) Students will have a classmate try their board to see if it can be solved before handing it in. (Revise) Students will have to practice how they are going to explain their board. (Rehearse) Teacher will allow students to work on board for homework for extra credit. (Refine)
12. Wiki reflection, quiz (Evaluate)
13. Mathematical/ Reasoning: Students will solve algebraic equations during class and while working on the interactive Tic-Tac-Toe board. Interpersonal: Students will be working in pairs. Intrapersonal: Students will be posting individual wiki reflection entries. Spacial/ Visual: Students will be making and sharing interactive boards. Musical/ Rhythmic: Background music will be playing while students work on their examples. Verbal/ Linguistic: Students will orally explain how their boards worked.
(Tailor)
14. Justify how visual representations are used to solve and express polynomial expressions. (Organize)
Lesson 3
Consider the W.H.E.R.E.T.O. elements. (L)
15. Students will understand how visual representations relate to polynomials expressions. (Where) This lesson is important to real life because it will connect the physical outside world to polynomials. (Why) Studentsunderstand and use polynomials and expressions with rational exponents. (What) Product: Excel matrix using class survey results.
16. Show a short video from TeacherTube about how polynomials relate to area models. (Hook)
17. Students should know the following terminology: polynomial function, FOIL method, leading term. Students should be able to solve basic polynomial expressions. (Equip) The beginning of the class will be a class discussion on how polynomials relate to visual models. (Explore) Students will share their matrix results with the class to show their understanding as an artifact that proves that they understand how a visual representation relates to a polynomial expressions. (Experience)
18. Sharing their matrix will allow them to explain the connection, and reflecting on the days work in a wiki post will allow students time to re-think. (Re-think) Students will have time to make corrections to their matrices after the class has presented. (Revise) Students will have to practice how they are going to explain their matrix. (Rehearse) Teacher will allow students to perfect their matrix for homework before posting it on the wiki. (Refine)
19. Wiki reflection (Evaluate)
20. Mathematical/ Reasoning: Students will solve a matrix equation. Interpersonal: Students will essentially be asking everyone in the class a question. Intrapersonal: Students will be posting individual wiki reflection entries. Physical/ Kinesthetic: Students will be going around the classroom surveying their classmates. Musical/ Rhythmic: Background music will be playing while students work on their examples. Naturalist: The survey is about the students favorite seasons. Verbal/ Linguistic: Students will write an entry in their wikis explaining their graphs and matrices.
(Tailor)
21. Relate the visual representations of polynomials to the mathematical solution. (Organize)
Lesson 4
Consider the W.H.E.R.E.T.O. elements. (L)
22. Students will understand how to choose which solution method is more appropriate for which polynomial application. (Where) This lesson is important to real life because it will enable students to pick which method is most efficient. (Why) Studentsunderstand and use polynomials and expressions with rational exponents. (What) Product: Short movie clip.
23. Comic Life about there being too many ways to do one thing. (Hook)
24. Students should know the following terminology: polynomial function, FOIL method, horizontal method, vertical method. Students should be able to solve basic polynomial expressions. (Equip) The beginning of the class will be a class discussion on how there are always more than one way to do a problem. (Explore) Students will share their short videos with the class to show their understanding as an artifact that proves that they understand which method is most appropriate for a particular application. (Experience)
25. Reflecting on the days work in a wiki post will allow students time to re-think. (Re-think) Students will have time to reflect on their work after watching the rest of the classes presentation. (Revise) Students will have to practice how they are going to explain their reasoning. (Rehearse) Teacher will allow students to tweak their videos for homework before posting it on the wiki. (Refine)
26. Rubric, wiki reflection (Evaluate)
27. Mathematical/ Reasoning: Students will do problem examples. Interpersonal: Students will work in pairs to make movie clip. Intrapersonal: Students will be posting individual wiki reflection entries. Physical/ Kinesthetic: Students will have the opportunity to do some acting or filming. Visual/ Spatial: Students will make and view a short video. Musical/ Rhythmic: Background music will be playing while students work on their videos; music could be included in videos. Verbal/ Linguistic: Students will write an entry in their wikis explaining their choices from their videos.
(Tailor)
28. Compare and choose which of the different solution methods for solving polynomial expressions best suits them. (Organize)
Lesson 5
Consider the W.H.E.R.E.T.O. elements. (L)
29. Students will be able to find some practical use of polynomials in the real world. (Where) This lesson is important because it's imperative that people make the connection on how to use polynomials in every day. (Why) Students understand and use polynomials and expressions with rational exponents. (What) Product: Excel shopping wishlist document
30. Cartoon about real world application of math. (Hook)
31. Students should know following vocabulary: polynomial function, constant term, "like" terms. Students should be able to solve basic polynomial expressions. (Equip) Students will share their findings with a partner. (Explore) Students will present their wishlist as an artifact that proves that they understand the practical uses of polynomials. (Experience)
32. Students will write a reflective wiki entry explaining product. (Re-think) Students will be allowed to continue working on the assignment for homework after peer reviewing with a partner. (Revise) Students will have to practice their explanation. (Rehearse) Students will have time to ask questions before posting the results onto their wiki. (Refine)
33. Wiki reflection, quiz (Evaluation)
34. Mathematical/ Reasoning: Students will be using algebra in finding the equations to express their wishlist. Musical/ Rhythmic: Background music will be playing while students work on their product. Naturalist: Students will have the opportunity to "shop" for summer things. Interpersonal: Students will be peer reviewing with a buddy. Intrapersonal: Students will have to work individually on their reflections and Excel. Spacial/ Visual: Students will have a visual matrix of their "shopping" results. Verbal/ Linguistic: Students will be writing a reflective wiki entry. Physical/ Kinestetic: Students will be moving around to choose their partners.
(Tailor)
35. Recognize some practical uses of polynomial functions in the real world. (Organization)
Lesson 6
Consider the W.H.E.R.E.T.O. elements. (L)
36. Students will be able to solve addition, subtraction, and multiplication problems that involve polynomials. (Where) The real life connection for this lesson has to do with the physical space that people live in. (Why) Students understand and use polynomials and expressions with rational exponents. (What) Product: Digital garden model
37. Video from the TV series Numb3rs about math being in everything (Hook)
38. Students should know vocabulary: polynomial function, linear function. Students should be able to add, subtract and multiply polynomial expressions. (Equip) Students will work in pairs on their presentation. (Explore) Students will present their models as an artifact that proves that they understand how polynomial expressions work together. (Experience)
39. The presentation will force them to explain the steps in the process of building the model, thus making them rethink the entire project. (Re-think) Students will use a check-in list to self-assess their work in order to make improvements. (Revise) Students will have to practice their presentation. (Rehearse) Teacher will give feedback on check-in list and work handed in half-way through project to give feedback. (Refine)
40. Rubric(s), check-in (Evaluate)
41. Mathematical/ Reasoning: Students will be using algebra in finding the dimensions of the garden. Physical/ Kinesthetic: Students will be working in pairs, and have the option to physically make something. Interpersonal: Students will be working in pairs. Intrapersonal: Students will have to work individually on their write ups. Spacial/ Visual: Students will have a visual model of their garden Naturalistic: Students will be learning about the process of gardening. Verbal/ Linguistic: Students will be writing a short explanation of their project and presenting it in front of the class. Musical/ Rhythmic: There will be music playing in the background while they work on their presentations.(Tailor)
42. Solve addition, subtraction, and multiplication problems that involve polynomials. (Organize)
Stage 3 Plan Learning Experiences and Instruction
1. (W) Where (Understanding), Why (Real Life), and What (MLR and Product)
2. (H) Hook (Engage)
3. (E) Equip (Instruction), Explore (Graphic Organizer), and Experience (Cooperative Learning)
4. (R) Rethink, Revise, Rehearse, and Refine (Timely Feedback)
5. (E) Evaluate (Self- Assessment)
6. (T) Tailor (Multiple Intelligences 6 to 8 and use each at least twice)
7. (O) Organize (Facet of Understanding)
Lesson 1
2. Read a poem aloud about math methods. (Hook)
3. Students should know the following terminology: "like" terms, polynomial, FOIL method, leading and constant term and polynomial function. Students should be able to at least add basic binomial expressions. (Equip) The beginning of the class will be a discussion and students with work in pairs discussing their wiki entry. (Explore) Students will share their examples with the rest of the class to show how each method can be used. (Experience)
4. The students will comment on each others' entries and say whether they agree or disagree and why; this will make students look at someone else's perspective. (Re-think) Students will have the opportunity to edit their entry should their peers' comments sway them. (Revise) Students will have to come up with examples of methods. (Rehearse) Students will be able to fix all grammatical and technical errors in wiki entries to receive full credit. (Refine)
5. Wiki reflection, KWL chart (Evaluate)
6. Mathematical/ Reasoning: Students will have to give examples on the wiki and why they work best.
Interpersonal: Students will be working in pairs on wiki entries.
Intrapersonal: Students will individually comment on their peers' wikis.
Spacial/ Visual: Students will take notes on the different methods shown written out on the board.
Verbal/ Linguistic: Students will be writing a small paragraph about math methods.
Musical/ Rhythmic: Students will listen to a poem about math. (Tailor)
7. Students will be able to illustrate how polynomial expressions can be solved using the horizontal, vertical or FOIL methods. (Organize)
Lesson 2
9. Draw a rectangle on the board and ask students to define what it is and what it could be. (Hook)
10. Students should know terminology: polynomial and "like" terms. Students should be able to solve basic polynomial expressions. (Equip) The beginning of the class will be a class discussion. (Explore) Students will present their Tic-Tac-Toe boards to show their understanding as an artifact that proves that they understand how a visual representation can be used to solve or express polynomial expressions. (Experience)
11. The presentation will force them to explain how they were able to figure out what box had to contain which equation. (Re-think) Students will have a classmate try their board to see if it can be solved before handing it in. (Revise) Students will have to practice how they are going to explain their board. (Rehearse) Teacher will allow students to work on board for homework for extra credit. (Refine)
12. Wiki reflection, quiz (Evaluate)
13. Mathematical/ Reasoning: Students will solve algebraic equations during class and while working on the interactive Tic-Tac-Toe board.
Interpersonal: Students will be working in pairs.
Intrapersonal: Students will be posting individual wiki reflection entries.
Spacial/ Visual: Students will be making and sharing interactive boards.
Musical/ Rhythmic: Background music will be playing while students work on their examples.
Verbal/ Linguistic: Students will orally explain how their boards worked.
(Tailor)
14. Justify how visual representations are used to solve and express polynomial expressions. (Organize)
Lesson 3
16. Show a short video from TeacherTube about how polynomials relate to area models. (Hook)
17. Students should know the following terminology: polynomial function, FOIL method, leading term. Students should be able to solve basic polynomial expressions. (Equip) The beginning of the class will be a class discussion on how polynomials relate to visual models. (Explore) Students will share their matrix results with the class to show their understanding as an artifact that proves that they understand how a visual representation relates to a polynomial expressions. (Experience)
18. Sharing their matrix will allow them to explain the connection, and reflecting on the days work in a wiki post will allow students time to re-think. (Re-think) Students will have time to make corrections to their matrices after the class has presented. (Revise) Students will have to practice how they are going to explain their matrix. (Rehearse) Teacher will allow students to perfect their matrix for homework before posting it on the wiki. (Refine)
19. Wiki reflection (Evaluate)
20. Mathematical/ Reasoning: Students will solve a matrix equation.
Interpersonal: Students will essentially be asking everyone in the class a question.
Intrapersonal: Students will be posting individual wiki reflection entries.
Physical/ Kinesthetic: Students will be going around the classroom surveying their classmates.
Musical/ Rhythmic: Background music will be playing while students work on their examples.
Naturalist: The survey is about the students favorite seasons.
Verbal/ Linguistic: Students will write an entry in their wikis explaining their graphs and matrices.
(Tailor)
21. Relate the visual representations of polynomials to the mathematical solution. (Organize)
Lesson 4
23. Comic Life about there being too many ways to do one thing. (Hook)
24. Students should know the following terminology: polynomial function, FOIL method, horizontal method, vertical method. Students should be able to solve basic polynomial expressions. (Equip) The beginning of the class will be a class discussion on how there are always more than one way to do a problem. (Explore) Students will share their short videos with the class to show their understanding as an artifact that proves that they understand which method is most appropriate for a particular application. (Experience)
25. Reflecting on the days work in a wiki post will allow students time to re-think. (Re-think) Students will have time to reflect on their work after watching the rest of the classes presentation. (Revise) Students will have to practice how they are going to explain their reasoning. (Rehearse) Teacher will allow students to tweak their videos for homework before posting it on the wiki. (Refine)
26. Rubric, wiki reflection (Evaluate)
27. Mathematical/ Reasoning: Students will do problem examples.
Interpersonal: Students will work in pairs to make movie clip.
Intrapersonal: Students will be posting individual wiki reflection entries.
Physical/ Kinesthetic: Students will have the opportunity to do some acting or filming.
Visual/ Spatial: Students will make and view a short video.
Musical/ Rhythmic: Background music will be playing while students work on their videos; music could be included in videos.
Verbal/ Linguistic: Students will write an entry in their wikis explaining their choices from their videos.
(Tailor)
28. Compare and choose which of the different solution methods for solving polynomial expressions best suits them. (Organize)
Lesson 5
30. Cartoon about real world application of math. (Hook)
31. Students should know following vocabulary: polynomial function, constant term, "like" terms. Students should be able to solve basic polynomial expressions. (Equip) Students will share their findings with a partner. (Explore) Students will present their wishlist as an artifact that proves that they understand the practical uses of polynomials. (Experience)
32. Students will write a reflective wiki entry explaining product. (Re-think) Students will be allowed to continue working on the assignment for homework after peer reviewing with a partner. (Revise) Students will have to practice their explanation. (Rehearse) Students will have time to ask questions before posting the results onto their wiki. (Refine)
33. Wiki reflection, quiz (Evaluation)
34. Mathematical/ Reasoning: Students will be using algebra in finding the equations to express their wishlist.
Musical/ Rhythmic: Background music will be playing while students work on their product.
Naturalist: Students will have the opportunity to "shop" for summer things.
Interpersonal: Students will be peer reviewing with a buddy.
Intrapersonal: Students will have to work individually on their reflections and Excel.
Spacial/ Visual: Students will have a visual matrix of their "shopping" results.
Verbal/ Linguistic: Students will be writing a reflective wiki entry.
Physical/ Kinestetic: Students will be moving around to choose their partners.
(Tailor)
35. Recognize some practical uses of polynomial functions in the real world. (Organization)
Lesson 6
37. Video from the TV series Numb3rs about math being in everything (Hook)
38. Students should know vocabulary: polynomial function, linear function. Students should be able to add, subtract and multiply polynomial expressions. (Equip) Students will work in pairs on their presentation. (Explore) Students will present their models as an artifact that proves that they understand how polynomial expressions work together. (Experience)
39. The presentation will force them to explain the steps in the process of building the model, thus making them rethink the entire project. (Re-think) Students will use a check-in list to self-assess their work in order to make improvements. (Revise) Students will have to practice their presentation. (Rehearse) Teacher will give feedback on check-in list and work handed in half-way through project to give feedback. (Refine)
40. Rubric(s), check-in (Evaluate)
41. Mathematical/ Reasoning: Students will be using algebra in finding the dimensions of the garden.
Physical/ Kinesthetic: Students will be working in pairs, and have the option to physically make something.
Interpersonal: Students will be working in pairs.
Intrapersonal: Students will have to work individually on their write ups.
Spacial/ Visual: Students will have a visual model of their garden
Naturalistic: Students will be learning about the process of gardening.
Verbal/ Linguistic: Students will be writing a short explanation of their project and presenting it in front of the class.
Musical/ Rhythmic: There will be music playing in the background while they work on their presentations.(Tailor)
42. Solve addition, subtraction, and multiplication problems that involve polynomials. (Organize)
2004 ASCD and Grant Wiggins and Jay McTighe